若函数 $f(x)=4 \cos (2 x+\varphi)-2 \sqrt{2}(0 \leq \varphi \leq \pi)$ 在 $\left[0, \frac{11 \pi}{6}\right]$ 内恰有 4 个零点, 则 $\varphi$ 的取值范围是
A
$\left[0, \frac{\pi}{4}\right] \cup\left[\frac{\pi}{2}, \frac{7 \pi}{12}\right]$
B
$\left[\frac{\pi}{12}, \frac{\pi}{4}\right] \cup\left[\frac{\pi}{2}, \frac{7 \pi}{12}\right]$
C
$\left[0, \frac{\pi}{4}\right] \cup\left[\frac{7 \pi}{12}, \pi\right]$
D
$\left[\frac{\pi}{12}, \frac{\pi}{4}\right] \cup\left[\frac{7 \pi}{12}, \pi\right]$
E
F